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Mere's Totally Random and (Mostly) Useless Maths Facts!

Yes and no..
Finding factors of very large numbers is actually still a big problem, as it is exponentially bigger than timing too numbers.
They are developing Quantum Computers (a lot of work on this is being done at my uni) which will be able to divide big numbers.

When are you required to divide big numbers in lets say a real life business situation?

Firstly, research isn't done and things aren't discovered for the purpose of real world applications. Applications can be diverse and abundant, but come much later. I'm sure people saw no purpose to Volta's was putting salt water soaked paper into between different metals, and alas 200 years later think of all the uses e have for a battery.

Secondly, this does have a use, the first part was just me being annoyed at your first statement.
If you multiple 2 large prime numbers say 50 digits plus, it is a lot quicker to calculate their product, rather than the factors on a number with over 100 digits. This fact is used in cryptology. Without going into is too much, if you wish to send a message, you encode in a way such that it is a 100 - 200 digit number even if anyone gets a hold of this number (message) there is no way for them to decode to it. Only the person who know the prime factor can decipher it.

Also "these computer" would revolutionize computing. Being able to do any calculation or execute any code and speeds near the speed of light.

"If functional quantum computers can be built, they will be valuable in factoring large numbers, and therefore extremely useful for decoding and encoding secret information. If one were to be built today, no information on the Internet would be safe. Our current methods of encryption are simple compared to the complicated methods possible in quantum computers. Quantum computers could also be used to search large databases in a fraction of the time that it would take a conventional computer."
I found this on online if you're interested Silent. http://ewh.ieee.org/r10/bombay/news4/Quantum_Computers.htm

Also research is mostly funded by big business, minorly funded by government, so having an idea that could affect big business (or military - like encryption) is actually a pretty big requirement in getting **** done.

Firstly, research isn't done and things aren't discovered for the purpose of real world applications. Applications can be diverse and abundant, but come much later. I'm sure people saw no purpose to Volta's was putting salt water soaked paper into between different metals, and alas 200 years later think of all the uses e have for a battery.

Secondly, this does have a use, the first part was just me being annoyed at your first statement.
If you multiple 2 large prime numbers say 50 digits plus, it is a lot quicker to calculate their product, rather than the factors on a number with over 100 digits. This fact is used in cryptology. Without going into is too much, if you wish to send a message, you encode in a way such that it is a 100 - 200 digit number even if anyone gets a hold of this number (message) there is no way for them to decode to it. Only the person who know the prime factor can decipher it.

Also "these computer" would revolutionize computing. Being able to do any calculation or execute any code and speeds near the speed of light.

I see value in real science, but these numbers that are still linear has very little value, like trying to calculate how large the universe is or getting a general arts degree vs. accelerating particles faster than light, y'know something that actually adds real world value.